It was well-known that higher-order interference such as Hong-Ou-Mandel (HOM) interference effect [1]}, [2]} does not rely on the coherence time of the fields in that interference even between independent fields may occur [3]}, [4]}. But such effect is insensitive to phase change of the fields. On the other hand, phase-dependent fourth-order interference effect occurs in Franson interferometer [5]} which consists of two highly imbalanced interferometers beyond coherence length [6]}, [7]}, [8]}. But it was shown that the effect exists only for two-photon quantum fields and disappears for stationary classical fields [9]}. The progress on the interference with imbalanced paths was halted until recently when it was reported that phase dependent fourth-order interference between two thermal fields can appear in the time-resolved coincidence between two detectors even when the path imbalance of the interferometer is well beyond the coherence length of the fields [10]}, [11]}. This leads to a huge advantage over the traditional interferometers based on second-order interference where interference appears in one detector and requires path imbalance between interfering fields be smaller than the coherence length of the fields.
